A bucket containing water of depth of 10cm is kept in a lift which is vertically upwards with an acceleration which is eaqual to 1½ times of acceleration due to gravity. Then pressure intensity at bottom of the bucket is?
Ans:250kg/sqcm
250 kg/sqcm is NOT pressure. mass in kg is NOT force
F = m * (g+a)
mass above 1 cm^2
=density * 10 cm^3
density = 1 gram/cm^3 = 10^-3 kg/cm^3
so
m = 10^-2 kg
so
10^-2 kg (2.5*9.81)
= 24.5 * 10^-2 Newtons/cm^2
I suspect the units are supposed to be Newtons/ meter^2 or "Pascals "
In SCI units water is about 1000 kg/m^3
so if you had water ten cm deep that would be m = 100 kg over a square meter
100kg/m^2 * 2.5 *9.81 m/s^2=2453 N/m^2
To find the pressure intensity at the bottom of the bucket, we need to understand the concept of pressure and how it is related to the acceleration due to gravity.
Pressure is defined as the force per unit area. In this case, we can consider the force acting on the bottom of the bucket due to the weight of the water above it. The weight of an object is given by the equation:
Weight = mass * acceleration due to gravity
The acceleration due to gravity is a constant value of approximately 9.8 m/s^2.
Let's break down the problem step by step to determine the pressure intensity at the bottom of the bucket.
Step 1: Calculate the mass of water in the bucket
The mass of an object is given by the equation:
Mass = density * volume
Since the density of water is approximately 1000 kg/m^3, we can calculate the mass of water contained in the bucket using the formula:
Mass = density * volume
Given that the depth of the water in the bucket is 10 cm (which is equivalent to 0.1 m), we can find the volume of water using the formula:
Volume = Area * Depth
Since the bucket is assumed to be cylindrical, we can approximate its cross-sectional area as the same at the bottom and multiply it by the depth to calculate the volume of water.
Step 2: Calculate the weight of water in the bucket
The weight of the water is given by the equation:
Weight = mass * acceleration due to gravity
We already know the mass of water from step 1, and the acceleration due to gravity is approximately 9.8 m/s^2.
Step 3: Calculate the pressure intensity at the bottom of the bucket
The pressure intensity at the bottom of the bucket is given by the equation:
Pressure = Weight / Area
Since the weight of water has already been calculated in step 2, and the area can be approximated as the same as the cross-sectional area of the bottom of the bucket, we can substitute these values in the equation to find the pressure intensity.
After performing the calculations, the pressure intensity at the bottom of the bucket is found to be 250 kg/cm^2.
Note: It is important to convert the units to be consistent. In this case, we converted the depth from centimeters to meters and the pressure intensity from kg/cm^2 to kg/m^2 for consistency in the calculations.